At this conference four years ago, a measurement of the ionization potential of $H_{2}$ accurate to $0.015 cm^{-1}$ was described. This talk will emphasize the rapid progress that has been made since then. The majority of recent experiments employ a two-step approach, in which highly excited levels are measured relative to the $EF (^{2}s\sigma)^{1}\Sigma^{+}_{g}$ state. The EF state energy levels are measured in a separate experiment. My research group has very recently succeeded in measuring two-photon $EF \leftarrow X$ intervals in $H_{2}, $HD, and $D_{2}$ to an accuracy of 0. 001 $cm^{-1}$, or 1 part in $10^{8}$. A pulse-amplified single-mode cw laser is used in a Doppler-free counterpropagating-beam configuration. The main difficulty is that substantial optical phase distortion occurs during pulsed amplification of a laser. To overcome this, we measure the optical phase directly using a heterodyne scheme. These measurements are thought to be the most accurate spectroscopic results ever obtained using pulsed lasers. From the EF state, higher Rydberg stales can he accessed. This allows both the investigation of excited-state structure and dynamics, and experimental determinations of the ionization potential and dissociation energy. During the past few years experiments of this type have been conducted both by Herzberg and $coworkers^{1}$ and by my own research $group.^{2}$ In this talk I will describe one example of this work, a measurement of the ionization potential of HD by extrapolation of the high Rydberg up $states.^{1}$ Agreement of theory With experiment is presently quite good, though there are hints of a possible small mass-dependent discrepancy. The hydrogen molecule thus continues to serve as one of the key benchmarks for testing molecular physics, including tests of quantum electrodynamics at the 5% level and beyond.